It's the best holiday of the year featuring the best dessert of all time and I have no oven - can I still make pumpkin pie?
Do you mean can you "bake" one on the stovetop instead? Probably not, since you won't be able to get an even, constant heat. What you can do is something like a set custard pie that doesn't need to be baked; buy a pre-made pie crust, and cook the filling, pour it into the crust and chill before serving. I haven't tried this one myself but I found it on allrecipes.com: http://allrecipes.com/Recipe...
A typical pumpkin pie is an egg custard, so you need to bake & set the eggs in some way - for food safety and texture reasons.
If you have a stovetop, you could possibly make a pumpkin cheesecake or pie filling-esque custard in a slow hot water bath (bain marie). Put the filling in a springform pan, lined tightly with cling film and then 2 layers of aluminum foil, or in individual ramekins and place in a pan with 4" sides. Fill the pan with hot, recently boiled water about 1/2 way up the sides of the dish(es) and cover the pan with foil. Keep on low heat and make sure the water continues to simmer while the custard bakes.
This won't work for a dessert with a traditional flaky pie crust, but you could maybe use a shards of pre-baked pie crust/puff pastry as a garnish or do a graham cracker crust base.
You could also try a pumpkin mousse:
As mentioned, you can do a graham cracker crust and use either a pumpkin/cheesecake or pumpkin pudding mixture as the filling.
A pumpkin trifle might be another option, though you'd probably have to opt for pumpkin bread or some other type of cake from your bakery or market.
Alternatively, you can make a pumpkin ice cream, served with roasted pumpkin or pumpkin seeds, granola, or any other topping you like.
Thought you might enjoy this pumpkin mousse instead:
If it's pumpkin pie you must have (not mousse, or any of the other good suggestions from other posters) - I suggest going to a good bakery and pick one up. It will be better than pie you could hack without an oven!
A prebaked crust (preferably a crumb crust, pumpkin mousse as filling -- smooth, chill, serve with whipped cream.
I think I found a good one: http://www.kitchendaily.com/recipe/frozen-pumpkin-mousse-pie-152161. Just skip the oven step.